Finite Group Databasebeta

← #28401321

Subgroups — #28401321

Order 14464.

520 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 121 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#121×D113C212yesmaximal, complemented
2#20298913C212yesmaximal, complemented
3#20298910C212yesmaximal, complemented
4#20298834C211yesmaximal, characteristic, complemented
5#20298832C212yesmaximal, complemented
6#20298733C212yesmaximal, complemented
7#20298730C212yesmaximal, complemented
8C2×#16813534C211yesmaximal, characteristic, complemented
9#466×C113C211yesmaximal, characteristic, complemented
10C2×D4×D113—22no—
11C2×D4×D113C2212yescomplemented
12C22×C4×D113C2211yescharacteristic
13C2×D904C2211yescharacteristic, complemented
14C2×#14268632C2212yescomplemented
15C22×#11744751C2211yescharacteristic, complemented
16#16813597C2212yes—
17#16813596C2212yescomplemented
18#16813595—22no—
19#16813594—22no—
20#16813593C2212yes—
21C4⋊C4×D113C2212yescomplemented
22C22⋊C4×D113—22no—
23#16813556C2211yescharacteristic, complemented
24#16813555C2212yescomplemented
25#16813544C2212yescomplemented
26#16813543C2212yescomplemented
27#16813542C2212yescomplemented
28#16813534C2212yescomplemented
29#16813534C2212yescomplemented
30C2×D8×C113C2211yescharacteristic, complemented
31C22×C8×C113C2211yescharacteristic, complemented
32#121×C113C2212yescomplemented
33#107×C113C2211yescharacteristic, complemented
34#102×C113C2212yescomplemented
35C23×D113—22no—
36C23×D113D411yescharacteristic
37C2×D452—22no—
38C2×D452C2312yes—
39C2×C22⋊D113—22no—
40C2×C22⋊D113—22no—
41C2×C22⋊D113—22no—
42D4×D113—42no—
43D4×D113—42no—
44D4×D113—48no—
45C22×Dic113D411yescharacteristic
46C2×C4×D113—22no—
47C2×C4×D113—41no—
48C2×C4×D113—41no—
49C2×C4×D113D412yes—
50C2×C4×D113C2312yes—
51D904—41no—
52#14268632—42no—
53C2×#11744751—41no—
54C2×#11744751C2312yes—
55C4⋊Dic113C2312yes—
56#14268626—22no—
57C22⋊Dic113—22no—
58#14268624—22no—
59#14268624—22no—
60C2×D4×C113—22no—
61C2×D4×C113C2312yes—
62C22×C4×C113C2311yescharacteristic
63D8×C113—41no—
64C2×C8×C113—41no—
65C2×C8×C113C2311yescharacteristic
66C2×C8×C113C2311yescharacteristic
67C4⋊C4×C113C2312yes—
68C22⋊C4×C113—22no—
69C23×C113—22no—
70C23×C113C2×D411yescharacteristic
71C22×D113—22no—
72C22×D113—41no—
73C22×D113—41no—
74C22×D113—44no—
75C22×D113—44no—
76C22×D113—44no—
77C22×D113D814yescomplemented
78C22×D113C2×D412yes—
79D4×C113—22no—
80D4×C113—22no—
81D4×C113—44no—
82C2×C4×C113—21no—
83C2×C4×C113—21no—
84C2×C4×C113—22no—
85C2×C4×C113C2×D411yescharacteristic
86C2×C4×C113C2411yescharacteristic
87C22⋊D113—44no—
88C22⋊D113—44no—
89C22⋊D113—44no—
90C2×Dic113—22no—
91C2×Dic113—41no—
92C2×Dic113C2×D412yes—
93D452—22no—
94D452—22no—
95D452—44no—
96C4×D113—22no—
97C4×D113—22no—
98C4×D113—42no—
99C4×D113—44no—
100C8×C113—21no—
101C8×C113—21no—
102#11744751—22no—
103C22×C113—21no—
104C22×C113—21no—
105C22×C113—42no—
106C22×C113—42no—
107C22×C113—42no—
108C22×C113C2×D812yes—
109C22×C113C22×D411yescharacteristic
110C2×D113—22no—
111C2×D113—22no—
112C2×D113—44no—
113C2×D113—42no—
114C2×D113—42no—
115C2×D113—42no—
116C2×D113—88no—
117C2×D113C2×D814yes—
118C4×C113—21no—
119C4×C113—42no—
120C4×C113H(5,𝔽2)11yescharacteristic
121C4×C113H(5,𝔽2)11yescharacteristic
122Dic113—22no—
123Dic113—42no—
124C2×C113—22no—
125C2×C113—82no—
126C2×C113#53411yescharacteristic
127C2×C113C22×D811yescharacteristic
128C2×C113#57511yescharacteristic
129D113—24no—
130D113—82no—
131#3186—1131nomaximal, Sylow
132C113#318611yescharacteristic, complemented, Sylow
133C2×#121—1132no—
134#480—1132no—
135#480—1132no—
136#466—1131no—
137#466—1132no—
138#466D11311yescharacteristic, complemented
139#447—1132no—
140#447—1132no—
141C2×C22⋊C8—1131no—
142C22×D4—1132no—
143C22×D4—2262no—
144C23×C4—1131no—
145C2×D8—1132no—
146C2×D8—1131no—
147C2×D8C2×D11311yescharacteristic, complemented
148C22×C8—1131no—
149C22×C8C2×D11311yescharacteristic, complemented
150#121—1132no—
151#121—1132no—
152#121—1132no—
153#121—2262no—
154#121—2262no—
155#121C2×D11312yescomplemented
156C2×C4⋊C4—1132no—
157C2×C22⋊C4—2262no—
158#107—1131no—
159#107—1132no—
160#107C2×D11311yescharacteristic, complemented
161#102—1132no—
162#102—1132no—
163#102—1132no—
164#102C2×D11312yescomplemented
165C22⋊C8—1132no—
166C22⋊C8—1132no—
167C24—1131no—
168C24—2262no—
169C2×D4—22no—
170C2×D4—1132no—
171C2×D4—4528no—
172C2×D4—4522no—
173C2×D4—4522no—
174C2×D4—2262no—
175C2×D4—2262no—
176C2×D4—2262no—
177C2×D4—2262no—
178C2×D4C22×D11312yes—
179C22×C4—1131no—
180C22×C4—1132no—
181C22×C4—1132no—
182C22×C4—4521no—
183C22×C4—4521no—
184C22×C4—2262no—
185C22×C4C22×D11311yescharacteristic
186D8—41no—
187D8—4521no—
188D8—4522no—
189C2×C8—41no—
190C2×C8—1132no—
191C2×C8—4521no—
192C2×C8C22×D11311yescharacteristic
193C2×C8C22×D11311yescharacteristic
194C4⋊C4—1132no—
195C4⋊C4—2262no—
196C4⋊C4C22×D11312yes—
197C22⋊C4—22no—
198C22⋊C4—2262no—
199C22⋊C4—2262no—
200C22⋊C4—2262no—
201C23—22no—
202C23—1134no—
203C23—1132no—
204C23—4521no—
205C23—4521no—
206C23—4524no—
207C23—4524no—
208C23—4524no—
209C23—2262no—
210C23D4×D11311yescharacteristic
211D4—22no—
212D4—22no—
213D4—44no—
214D4—4524no—
215D4—4524no—
216D4—4524no—
217D4—4524no—
218D4—2262no—
219D4—2262no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—22no—
223C2×C4—1132no—
224C2×C4—4522no—
225C2×C4—4524no—
226C2×C4—4521no—
227C2×C4—2262no—
228C2×C4—2262no—
229C2×C4—2262no—
230C2×C4D4×D11311yescharacteristic
231C2×C4C23×D11311yescharacteristic
232C8—21no—
233C8—21no—
234C8—2262no—
235C22—21no—
236C22—21no—
237C22—42no—
238C22—42no—
239C22—42no—
240C22—1134no—
241C22—9048no—
242C22—4524no—
243C22—4522no—
244C22—4522no—
245C22—4522no—
246C22—2262no—
247C22—2262no—
248C22D8×D11312yes—
249C22C2×D4×D11311yescharacteristic
250C4—21no—
251C4—42no—
252C4—4522no—
253C4—2262no—
254C4#1681366711yescharacteristic
255C4#1681366811yescharacteristic
256C2—22no—
257C2—82no—
258C2—9042no—
259C2—2264no—
260C2#2029915611yescharacteristic
261C2C2×D8×D11311yescharacteristic
262C2#2029939511yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#466×C113C2
socleC22×C113C22×D4
hypercenter#466D113
hypocenterC113#3186
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #121×D113C2semidirect
2. #20298913C2semidirect
3. #20298910C2semidirect
4. #20298834C2semidirect
5. #20298832C2semidirect
6. #20298733C2semidirect
7. #20298730C2semidirect
8. C2×#16813534C2semidirect
9. #466×C113C2semidirect
11. C2×D4×D113C22semidirect
13. C2×D904C22semidirect
14. C2×#14268632C22semidirect
15. C22×#11744751C22semidirect
17. #16813596C22semidirect
21. C4⋊C4×D113C22semidirect
23. #16813556C22semidirect
24. #16813555C22semidirect
25. #16813544C22semidirect
26. #16813543C22semidirect
27. #16813542C22semidirect
28. #16813534C22semidirect
29. #16813534C22semidirect
30. C2×D8×C113C22semidirect
31. C22×C8×C113C22semidirect
32. #121×C113C22semidirect
33. #107×C113C22semidirect
34. #102×C113C22semidirect
77. C22×D113D8semidirect
132. C113#3186semidirect
138. #466D113semidirect
147. C2×D8C2×D113semidirect
149. C22×C8C2×D113semidirect
155. #121C2×D113semidirect
160. #107C2×D113semidirect
164. #102C2×D113semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#121×D1132
#202989132
#202989102
#202988342
#202988322
#202987332
#202987302
C2×#168135342
#466×C1132
#3186113